What is the Scientific Notation Formula? Understand the Steps with Real Life Examples.

Introduction

In this article, you will learn the scientific notation formula to express a quantity in a simple form. Moreover, you will also learn what are the 5 rules of scientific notation.

What is Scientific Notation?

It is a simple but scientific way of writing very small or very large numbers in a short form. It is a way of expressing largest and smallest quantities as a number with significant digits. Scientific notation has made it easier to write very large or small numbers using significant digits.

In physics, the scientific notation is mostly used by scientists in order to find the nearest approximation of different results. This nearest approximation helps them to compare different experimental quantities.

Scientific Notation Formula

There are two parts of scientific notation coefficient between 1 but less than 10 and the power of 10. The coefficient has a whole part that is left to the decimal point and right to the decimal known as mantissa.

The standard form of scientific notation for a number N can be written as;

What are three Steps to Scientific Notation?

Suppose the scientific notation for a number n can be written as the power of 10. Then to approximate this number, the formula for scientific notation is,

$$N\;=\;n\;×\;10^x$$

To determine scientific notation of a quantity, the following three steps can be performed.

Move the decimal point to the left side if the number is large, otherwise move to the right side and stop moving just before the last non-zero digit.
Place the decimal point after the last non-zero digit of the number and count the number of digits that you moved.
Write the number in scientific notation with the power of 10.

Let’s discuss how to write in scientific notation in the following examples.

Scientific Notation Examples in Real Life

The distance between the Sun and Earth is 151,650,000,000 km. It is a large number that can be written in a simple way by using scientific notation such that 1.51×10¹¹km.
The mass of average human cell is 0.000000000001 kg which is smallest number and can be express as the power of 10 such that 110^-12kg. The negative sign indicates that the number is a small number.
A computer hard disk could hold 4 gigabytes about 4,000,000,000 bytes of information. In scientific notation, we can write it as 4.0 × 10⁹ bytes.

Formulas Related to Scientific Notation Formula

Order of magnitude

The order of magnitude gives the idea about how big a small object is. According to the definition of order of magnitude, a number N in the form can be written in a scientific form, there exist a number x such that 0.5 < n ≤ 5 so,

N = n × 10^x

Significant Figures

Every non-zero number is a significant number. For example, in 54.0 the significant digits are 2. Zero is not significant if it is after a decimal point.

FAQ's on Scientific Notation Formula

What are the 5 Rules of Scientific Notation?

There are five rules of writing a number by using scientific notation. These are;

The base should always be 10.
The exponent must be a non-zero integer, which means it can be either positive or negative.
The absolute value of the coefficient is greater than or equal to 1, but it should be less than 10.
Coefficients can be positive or negative numbers, including whole and decimal numbers.
The mantissa carries the rest of the significant digits of the number.

What is the Scientific Notation of 64120?

To write the given number in scientific notation, you can perform the following steps.

Move the decimal to the left side and stop just before 6.
Count the number of digits that you moved from the left side. The number of digits is 4.
Write 64120 in decimal form as the power of 10 such that,

$$6.412\;×\;10^4$$

What is Scientific Notation in Math?

It is a way of writing very large or small numbers in a short and simple form. It is a scientific way of writing experimental quantities. It helps to compare two or more quantities in order to find the nearest exact approximation.